We construct an eigenvalue problem by confining many-body system to a bounded domain with the boundary condition that the wave function vanishes. By changing the boundary, however, the eigenvalues of the energy can be varied continuously. The D-matrix is defined for a series of bounded problems with the same value for the ground state energy. The D-matrix is related to the S-matrix, enabling us to calculate the S-matrix at a given energy. The Schrodinger equation for the system is transformed to a diffusion equation by regarding time as imaginary. Initial ensemble, representing an approximate wave function, is evolved, through Monte Carlo simulation of random walks and branching, to the ground state ensemble. The limitations of investigation are: 1. Ingoing and outgoing channels have two fragments. 2. The interaction between the fragments is negligible outside the boundary mentioned above. 3. The particles are bosons or we know the zeros of the wave function.
First we consider the scattering of a particle by a potential, which is equivalent to the two-body problem, in one dimension. Here we use the Poschl-Teller potential for which the exact solution is known. We use this case to investigate a new sampling method and study of various parameters. Next we consider three particles in one dimension. Here we take interaction to be a potential well, where at least one of the interactions is attractive so that a two-body bound state is possible.
